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Table 4 Temporal convergence rates for Example 3, with \(\Delta x=\Delta y=\frac{1}{160}\) and \(\nu =0.01\)

From: Numerical solution of advection–diffusion type equation by modified error correction scheme

h t = 0.5 t = 2.0
u v u v
\(\mathit {err}_{R2}(t)\) Rates \(\mathit {err}_{R2}(t)\) Rates \(\mathit {err}_{R2}(t)\) Rates \(\mathit {err}_{R2}(t)\) Rates
\(\frac{1}{80}\) 2.50 × 10−4 1.67 × 10−4 4.28 × 10−4 2.38 × 10−4
\(\frac{1}{160}\) 1.75 × 10−4 0.51 1.17 × 10−4 0.51 2.38 × 10−4 0.85 1.32 × 10−4 0.85
\(\frac{1}{320}\) 9.89 × 10−7 7.47 6.61 × 10−7 7.47 8.14 × 10−7 8.19 4.53 × 10−7 8.19
\(\frac{1}{640}\) 4.28 × 10−7 1.21 2.86 × 10−7 1.21 3.52 × 10−7 1.21 1.96 × 10−7 1.21
\(\frac{1}{1280}\) 1.22 × 10−7 1.81 8.14 × 10−8 1.81 9.94 × 10−8 1.82 5.53 × 10−8 1.82
\(\frac{1}{2560}\) 2.77 × 10−8 2.14 1.85 × 10−8 2.14 2.22 × 10−8 2.16 1.24 × 10−8 2.16